Much has changed since the electric energy industry has introduced distribution factors-based methods for monitoring line flows in large electric energy grids. The industry currently lacks sharing of information between different utilities and control areas. As a consequence, often the least expensive and cleanest resources cannot be scheduled to avoid possible transmission line flow congestion due to lack of such information exchange. Moreover, much industry effort has gone toward tracking different power transactions in order to ensure that these do not create thermal line flow overloads, in particular, namely to ensure no (N−1) security problems. An electrical power system is N−1 secure if any single component in the electrical power system can fail without affecting service to the consumers for at least thirty minutes following the component failure. The hybrid approach to regulated transmission and competitive generation has created many financial distortions as well. Nevertheless, short of any other known way of ensuring most efficient utilization of transmission assets for enabling efficient energy resource utilization, transmission owners build assets, system operators dispatch power around the anticipated transmission congestion limitations and the congestion cost is not directly used to give incentives for reducing congestion in the future.
As these and similar problems continue to create operating and planning problems, very little rethinking of the overall approach to monitoring and managing transmission system congestion has been done. As a result, it has become practically impossible to reconcile the use of sensors and controllers of the individual equipment with the objectives of operating and planning an electrical power system according to the coarse scalar measures such as (N−1) security objectives. Many developers of high technologies with a potential for enhancing effectiveness of future power grid operations currently provide ready-to-use and cost-effective sensors, communications and decision tools with large computing power at the equipment level. The ultimate vision of micro-grids as almost entirely autonomous self-adjusting networks enabling utilization of many small distributed energy resources and meeting diverse energy needs of consumers has remained a remote dream given the wide gap between the methods used to monitor and manage resources and the methods which could be used to take advantage of smart distributed sensors and controllers.
Today's industry typically uses tools, such as distribution factors, to make adjustments to the system. The distribution factors measure how sensitive changes in each line's flow are to changes in each injection at the buses of the system. When generation is to be adjusted at individual buses, the change in each line flow can be inferred using the distribution factors, to check if line flows will violate line constraints, such as physical or thermal limits.
The power injections to the buses denoted here as vector Pg, and the phase angles at the nodes denoted as vector 8, then are related as follows:Pg=B′θ,  (1)where B′ is a full susceptance matrix of the system. Since one nodal phase angle will be dependent on other nodal phase angles, the full susceptance matrix will be a singular matrix. The full susceptance matrix usually has the first row removed since a first node corresponds to a slack bus. The first column of the full susceptance matrix is removed as well.
On the other hand, the relationship between the nodal angles θ and the line flows Pƒ can be written asPƒ=DAθ,  (2)where D is a diagonal matrix whose diagonal elements are the negative of the susceptance of a line corresponding to an associated branch. The matrix A is the line-node incidence matrix. In combining the equation (1) and the equation (2), a relationship between Pƒ and Pg is expressed asPƒ=DAB″−1Pg.  (3)
Equation (3) shows the sensitivity of Pƒ to Pg for a given network, and it is routinely used by the industry to relate incremental changes in line flows created by the incremental changes in power injections. A matrix that relates Pƒ to Pg is often referred to as the distribution factors matrix.
Network operators will need to know the entire A matrix as well as to invert the full susceptance matrix in order to perform a distribution factor calculation. Then, if thermal line flow constraints are violated, the network operators will need to adjust injections until the line constraints are no longer violated.